- The Oxford Handbook of Probability and Philosophy
- List of Contributors
- Introduction
- Probability for Everyone—Even Philosophers
- Pre-history of Probability
- Probability in 17th- and 18th-century Continental Europe from the Perspective of Jacob Bernoulli’s <i>Art of Conjecturing</i>
- Probability and Its Application in Britain during the 17th and 18th Centuries
- A Brief History of Probability Theory from 1810 to 1940
- The Origins of Modern Statistics: The English Statistical School
- The Origins of Probabilistic Epistemology: Some Leading 20th-century Philosophers of Probability
- Kolmogorov’s Axiomatization and Its Discontents
- Conditional Probability
- The Bayesian Network Story
- Mathematical Alternatives to Standard Probability that Provide Selectable Degrees of Precision
- Probability and Nonclassical Logic
- A Logic of Comparative Support: Qualitative Conditional Probability Relations Representable by Popper Functions
- Imprecise and Indeterminate Probabilities
- Symmetry Arguments in Probability
- Frequentism
- Subjectivism
- Bayesianism vs. Frequentism in Statistical Inference
- The Propensity Interpretation
- Best System Approaches to Chance
- Probability and Randomness
- Chance and Determinism
- Human Understandings of Probability
- Probability Elicitation
- Probabilistic Opinion Pooling
- Quantum Probability: An Introduction
- Probabilities in Statistical Mechanics
- Probability in Biology: The Case of Fitness
- Probability in Epistemology
- Confirmation Theory
- Self-Locating Credences
- Probability in Logic
- Probability in Ethics
- Probability and the Philosophy of Religion
- Probability in Philosophy of Language
- Decision Theory
- Probabilistic Causation
- Name Index
- Subject Index

## Abstract and Keywords

This chapter challenges the nearly universal reliance upon standard mathematical probability for mathematical modeling of chance and uncertain phenomena, and offers four alternatives. In standard practice, precise assignments are made inappropriately, even to the occurrences of events that may be unobservable in principle. Four familiar examples of chance or uncertain phenomena are discussed, about which this is true. The theory of measurement provides an understanding of the relationship between the accuracy of information and the precision with which the phenomenon under examination should be modeled mathematically. The model of modal or classificatory probability offers the least precision. Comparative probability, plausibility/belief functions and upper/lower probabilities are carefully considered. The selectable precision of these alternative mathematical models of chance and uncertainty makes for an improved range of levels of accuracy in modeling the empirical domain phenomena of chance, uncertainty, and indeterminacy. Knowledge of such models encourages further thought in this direction.

Keywords: courtroom, climate forecast, precision, measurement, frequentist, subjectivist, comparative probability, plausibility function, envelope of probability, tail event

Terrence Fine, School of ECE & Department of Statistical Sciences, Cornell University

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- The Oxford Handbook of Probability and Philosophy
- List of Contributors
- Introduction
- Probability for Everyone—Even Philosophers
- Pre-history of Probability
- Probability in 17th- and 18th-century Continental Europe from the Perspective of Jacob Bernoulli’s <i>Art of Conjecturing</i>
- Probability and Its Application in Britain during the 17th and 18th Centuries
- A Brief History of Probability Theory from 1810 to 1940
- The Origins of Modern Statistics: The English Statistical School
- The Origins of Probabilistic Epistemology: Some Leading 20th-century Philosophers of Probability
- Kolmogorov’s Axiomatization and Its Discontents
- Conditional Probability
- The Bayesian Network Story
- Mathematical Alternatives to Standard Probability that Provide Selectable Degrees of Precision
- Probability and Nonclassical Logic
- A Logic of Comparative Support: Qualitative Conditional Probability Relations Representable by Popper Functions
- Imprecise and Indeterminate Probabilities
- Symmetry Arguments in Probability
- Frequentism
- Subjectivism
- Bayesianism vs. Frequentism in Statistical Inference
- The Propensity Interpretation
- Best System Approaches to Chance
- Probability and Randomness
- Chance and Determinism
- Human Understandings of Probability
- Probability Elicitation
- Probabilistic Opinion Pooling
- Quantum Probability: An Introduction
- Probabilities in Statistical Mechanics
- Probability in Biology: The Case of Fitness
- Probability in Epistemology
- Confirmation Theory
- Self-Locating Credences
- Probability in Logic
- Probability in Ethics
- Probability and the Philosophy of Religion
- Probability in Philosophy of Language
- Decision Theory
- Probabilistic Causation
- Name Index
- Subject Index